






"""simple docstring"""
import unittest

from transformers import is_tf_available
from transformers.testing_utils import require_tf


if is_tf_available():
 import tensorflow as tf
 from tensorflow.python.eager import context
 from tensorflow.python.framework import ops

 from transformers import GradientAccumulator, create_optimizer



@require_tf
class        UpperCamelCase__ (				unittest.TestCase):







    """simple docstring"""







    def 				a__			(		self :	Optional[Any]				,    UpperCamelCase_ :	Any				,    UpperCamelCase_ :	int				,    UpperCamelCase_ :	int ):





           '''simple docstring'''

           self.assertEqual(len(UpperCamelCase_ )				,    len(UpperCamelCase_ ) )
           for a, b in zip(UpperCamelCase_				,    UpperCamelCase_ ):
                  self.assertAlmostEqual(UpperCamelCase_				,    UpperCamelCase_				,    delta=UpperCamelCase_ )







    def 				a__			(		self :	Tuple ):





           '''simple docstring'''

           __magic_name__      				=    GradientAccumulator()
           accumulator([tf.constant([1.0, 2.0] )] )
           accumulator([tf.constant([-2.0, 1.0] )] )
           accumulator([tf.constant([-1.0, 2.0] )] )
           with self.assertRaises(UpperCamelCase_ ):
                  accumulator([tf.constant([1.0, 1.0] ), tf.constant([2.0, 2.0] )] )
           self.assertEqual(accumulator.step				,    3 )
           self.assertEqual(len(accumulator.gradients )				,    1 )
           self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist()				,    [-2.0, 5.0]				,    tol=1e-2 )
           accumulator.reset()
           self.assertEqual(accumulator.step				,    0 )
           self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist()				,    [0.0, 0.0]				,    tol=1e-2 )







    def 				a__			(		self :	List[Any] ):





           '''simple docstring'''

           __magic_name__      				=    None
           ops.enable_eager_execution_internal()
           __magic_name__      				=    tf.config.list_physical_devices('CPU' )
           if len(UpperCamelCase_ ) == 1:
                  tf.config.set_logical_device_configuration(
                      physical_devices[0]				,    [tf.config.LogicalDeviceConfiguration(), tf.config.LogicalDeviceConfiguration()] )
           __magic_name__      				=    tf.config.list_logical_devices(device_type='CPU' )
           __magic_name__      				=    tf.distribute.MirroredStrategy(devices=devices[:2] )

           with strategy.scope():
                  __magic_name__      				=    GradientAccumulator()
                  __magic_name__      				=    tf.Variable([4.0, 3.0] )
                  __magic_name__				,  __magic_name__      				=    create_optimizer(5e-5				,    1_0				,    5 )
                  __magic_name__      				=    tf.Variable([0.0, 0.0]				,    trainable=UpperCamelCase_ )

           def accumulate_on_replica(UpperCamelCase_ :	str ):
                  accumulator([gradient] )

           def apply_on_replica():
                  optimizer.apply_gradients(list(zip(accumulator.gradients				,    [variable] ) ) )

           @tf.function
           def accumulate(UpperCamelCase_ :	Dict				,    UpperCamelCase_ :	Union[str, Any] ):
                  with strategy.scope():
                         __magic_name__      				=    strategy.experimental_local_results(UpperCamelCase_ )
                         local_variables[0].assign(UpperCamelCase_ )
                         local_variables[1].assign(UpperCamelCase_ )
                         strategy.run(UpperCamelCase_				,    args=(gradient_placeholder,) )

           @tf.function
           def apply_grad():
                  with strategy.scope():
                         strategy.run(UpperCamelCase_ )

           def _check_local_values(UpperCamelCase_ :	List[Any]				,    UpperCamelCase_ :	Optional[int] ):
                  __magic_name__      				=    strategy.experimental_local_results(accumulator._gradients[0] )
                  self.assertListAlmostEqual(values[0].value()				,    UpperCamelCase_				,    tol=1e-2 )
                  self.assertListAlmostEqual(values[1].value()				,    UpperCamelCase_				,    tol=1e-2 )

           accumulate([1.0, 2.0]				,    [-1.0, 1.0] )
           accumulate([3.0, -1.0]				,    [-1.0, -1.0] )
           accumulate([-2.0, 2.0]				,    [3.0, -2.0] )
           self.assertEqual(accumulator.step				,    3 )
           _check_local_values([2.0, 3.0]				,    [1.0, -2.0] )
           apply_grad()
           self.assertListAlmostEqual(variable.value()				,    [4.0, 3.0]				,    tol=1e-2 )
           accumulator.reset()
           self.assertEqual(accumulator.step				,    0 )
           _check_local_values([0.0, 0.0]				,    [0.0, 0.0] )







"""simple docstring"""
def 							A						(				__snake_case: int = 1_0_0_0_0_0_0  )    ->		int:

       """simple docstring"""





       __magic_name__      				=    limit + 1
       __magic_name__      				=    [0] * limit
       for first_term in range(1 ,     __snake_case  ):
              for n in range(__snake_case ,     __snake_case ,     __snake_case  ):
                     __magic_name__      				=    first_term + n / first_term
                     if common_difference % 4:  # d must be divisble by 4
                            continue
                     else:
                            common_difference /= 4
                            if (
                                first_term > common_difference
                                and first_term < 4 * common_difference
                            ):  # since x,y,z are positive integers
                                   frequency[n] += 1  # so z>0 and a>d ,also 4d<a

       __magic_name__      				=    sum(1 for x in frequency[1:limit] if x == 1_0  )

       return count


if __name__ == "__main__":
 print(f"""{solution() = }""")